Logic as relations of ideas in Hume

Here are some quick screen shots of my notes on relations of ideas. I'll upload proper scans when I get a chance.

Quine's _Elementary logic_

The little logic textbook I wish I'd written was published in the 1940s by Quine. I'm using it to teach logic this semester (along with supplemental texts that do more formal things). I figured it would be useful to create screencasts on my iPad as I walk through the book. Those will be parked at my YouTube channel, and embedded at The Smokr Tumblr, the media-robust sibling to this journal. Here's a link to the first video, if you're interested.

More stacker toys

More video posts (they run 11 total--I'll clean all that up later...) at The Smokr Tumblr.

Stacker toys

Stacker toys raise a number of logically interesting challenges, especially if you try to use them as logical models and in logic games. A first look is at The Smokr Tumblr (5 video posts).

Geometric Stacker models

Melissa and Doug's Geometric Stackers on my workbench. A piece or two is missing from peg 3, btw.

I don't recall playing with stacker toys as a kid. Blocks, play-doh, stuff like that, but toys where you stack wood pieces on pegs didn't show up on my radar until I started using them in work on logic.

As part of a larger research problem I'm exploring on the logic of toys, I have some questions about stackers. But first a few observations.

Two obvious big facts about stackers. First, there are lots of brightly colored, variously shaped pieces (they have holes in them that accommodate the pegs they are stacked on). And second, there are those pegs. The pegs force the pieces into some arrangement or other, but the pieces have their various properties independent of their arrangement.

The stackers thus permit a grid system: peg 1, first position--perhaps 1.A, something like that--and on in the obvious way: 1.A, 1.B, 1.C, and so on. The height of the peg and the thickness (height) of each piece, if they are all similar, thus determine how many slots each peg has.

Suppose we create a model as our initial state in which piece a and piece b, both circular, are stacked on peg 1 in the first two positions (1.A and 1.B). Then suppose we create a model to be our final state, in which piece a is still at 1.A, but octagonal piece c is at 2.A and octagonal piece d is at 3.A. (Sorry--next time I'll have more pics. Maybe I'll move this discussion to my Tumblr blog.)

I'll hold off on the list of sentences in the model until Tumblr. For now, let me point out a couple of constraints on the Stackers:

1. The universe has pegs, numbered/slotted into a grid system (as I've been suggesting).
2. It will help enormously to have functions to make instructions simpler: $remove _top-most_ piece _early-most_$. The $_top-most_$ function is a space function (describing location in space), while the $_early-most_$ function is a time function (describing position in time).

Enough for now. 

Logic and writing templates

The little writing book _They say, I say_ is a very pleasant surprise. A colleague recommended I use it in the senior capstone seminar I'm teaching this semester, and so I adopted it sight unseen. I just got it today, and I can tell I'll like it very much.

A few thoughts, prompted as I read the introduction.

[1] Writing templates---strings such as "some object that... though I concede that... I still maintain that..."---serve an obvious practical goal, which I applaud. But they also raise an interesting side question about how logic and rhetoric are intertwined.

The "..." in the templates are obviously meant to be replaced by some content; hence they are extra-logical. But that means that logical bits are needed to create the desired relationships among those contents expressed in the total information. But the templates include rhetorical bits that do some of that work. "Though I concede that" has both a _logical form_, when combined with the informational content suppressed as "...", as well as a _capacity to help persuade the hearer_ to agree to some view (or at least---presumably---to be sympathetic to that view). 

What feature of "though I concede that..." carries the logical information, and what feature carries the rhetorical information? Classic pragmatic-semantic interface issues. I wonder how students "feel" that issue play out as they write.

[2] The authors stress heavily that writing is dialectical---a push-pull between writer as reader (capturing what "they say") and writer as writer (putting forth what "I say"). It occurs to me that there are several ways to flesh this out. The dialectic can be _adversarial_, _synthetic_, _analytic_, or maybe some other way altogether.

The adversarial dialectic pits opposing views against one another. The (hopeful) result is a "push upward"---that is, a resultant force responding to the force due to the feeder forces. The "new truth" is widely seen by its advocates as correcting certain excesses in the philosophy of logic and knowledge---the sort of thing we might suppose Socrates to have gotten right, and many of the rest of us to have gotten wrong. The synthetic dialectic is similar, but the emphasis is on the co-making of that resultant force. The analytic dialectic, unlike the other two, can be thought of as a synthetic dialectic with a downward arrow, if you'll allow me to continue the slightly opaque metaphor. That is, the push is really a pull down toward that which is fundamental.

The abstract inference that occurs to me: Push in this context can be thought of as encryption, pull as extraction. Writing then is a back-and-forth between encrypting processes applied to information, and extracting processes likewise applied to information.

The less abstract punch line: a writer aims at the spot where a bit of information shows more than anyone has a right to expect.

Descartes' logic

“When I was younger, my philosophical studies had included some logic...”

I have to confess this is my biggest disappointment with D and many of his contemporaries. For such a tremendous period in philosophy, there is little of value achieved in logic. So much of what is thought of as logic is really advice for being reasonable, or rules for argument and debate. It’s the most barren period in the history of logic I can think of, given the extraordinary work going on in metaphysics and epistemology. And its even more striking given the explosion in maths (Leibniz and Newton and their weird competition over the calculus, most notably).

Now that I mention it, I wonder how unusual that moment was for logic. It’s the strangest thing, frankly.

Contrast this with the recent denial of the logic/rhetoric distinction (say, by Derrida and others). That denial is surely unsound, but it can only be made with any force in a context where the distinction is well-understood, or at least widely held, as it is in mainstream logic and philosophy in the twentieth century. D and his contemporaries, at least if the Port-Royal Logic is typical, did not widely believe in the (strong) distinction. The Stoics, the Aristotelians, the Platonists, by contrast, did make the distinction, and had to fend off the deconstructivists of their day, the Sophists, who denied it. With the distinction comes the denial, I guess. (Hmm—I’ll have to fact-check this more.)

“...I had to seek some other method comprising the advantages of [logic, geometry, and algebra] but free from their defects.”

Of course, by ‘defects’ here D means something like uselessness, or else that they do little to cultivate the mind. Here is more evidence for my reading of D’s theory of logic as guidance for good thinking.